Dad here as well and while there are a few actual tricks (which you can google and add to your arsenal), what I found was to approach it as a puzzle and try some logical things first (wet/soiled?, hungry?, needs burped?, over-tired?, too hot? [rare], too cold? [less rare]) and if it wasn't one of those, well then here we go: just keep trying things somewhat randomly, taking notes later as to what worked and what didn't. Some kids like to be squeezed, others talked to, others picked up, others tickled, others rocked, and it changes 15-minute to 15-minute period.

My wife was better at some aspects or episodes than I was (especially if it was feeding as I could feed from a bottle eventually once I thawed and warmed and bottled the milk, but that took an eternity in crying infant terms), but I was better at staying calm and intrigued by how to solve the puzzle this time. If she got upset/frustrated because our infant was upset, nothing good came of it, and I am personality-wise better suited to plowing through that situation without [much visible] frustration.

Assuming it's not a fatal problem, eventually something will work; in the history of the world, that's never failed to be true.